Wait a second.
1) IIS does not connect to any RDBMS, except for storing session state - it is only a setting you can use in your application
2) SQL Express does not enable TCP/IP connector by default, you need to
enable it[
^].
3) For this to work, you need to have
specific port level access[
^] between the server running IIS and SQL Server - if they do not run on the same machine
4) In IIS applications run under application pools, that impersonate either a dedicated pool user or the authenticated client user (if NTLM or Kerberos is used). Kerberos is needed for delegation - if IIS needs to pass the client token to third party machine (running SQL server for example) delegation, thus Kerberos is needed. Integrated security authentication means delegation if the application is running under client user identity.
5) Either dedicated pool identity or client identity - integrated security implies that this user has to have access to SQL Server and the database of course.
So... check these...